ON SOLUTIONS TO THE TIME-FRACTIONAL NAVIER–STOKES EQUATIONS WITH DAMPING

Abstract

We deal with the time-fractional Navier–Stokes equations with damping in a bounded domain $\mathrm{\Omega }$ in ${ℝ}^3$. First, we establish the existence of weak solutions by Galerkin approximation for $\beta \ge 1$. We also show the uniqueness of weak solutions for $\beta \ge 4$. Further, we prove the regularity of the solution for $\beta \ge 3$ and .